Universality in escape from a modulated potential well

TL;DR

This paper investigates how the escape rate from a modulated potential well scales with modulation amplitude, revealing a universal behavior and a crossover in scaling exponents near the bifurcation point.

Contribution

The study combines experimental measurements and theoretical analysis to identify a universal scaling law for escape rates in periodically modulated potentials.

Findings

Measured ln W scales as (A_c - A)^{1.5} in experiments.

Theoretical prediction confirms a 3/2 scaling exponent in the adiabatic limit.

A crossover to a 2 scaling exponent occurs near the bifurcation point.

Abstract

We show that the rate of activated escape $W$ from a periodically modulated potential displays scaling behavior versus modulation amplitude $A$. For adiabatic modulation of an optically trapped Brownian particle, measurements yield $\ln W\propto (A_{\rm c} - A)^{\mu}$ with $\mu = 1.5$. The theory gives $\mu=3/2$ in the adiabatic limit and predicts a crossover to $\mu=2$ scaling as $A$ approaches the bifurcation point where the metastable state disappears.